Question

How do you find the domain and range of `g(x) = 2(1/2)^(2x) +3`?

Answer 1

`"Domain":(-∞,∞)`
`"Range":(3,∞)`

Explanation:

The Domain for almost any exponential function is `(-∞,∞)`.

For the Range, find the asymptote to help.

The asymptote is `y=3`.

The asymptote means a line that the exponential function will always get closer to, but will never touch (graphing calculators will round it off eventually though).

Since the function is decreasing from infinity, the range is `(3,∞)`

Here is a graph:

graph{2*(1/2)^(2x)+3 [-10, 10, -5, 5]}